Where does staff fall under Traveller?
In CT? Probably under Brawling:
LBB1: "Brawling: Brawling is a general skill for hand-to-hand combat. It includes the use of hands, clubs, and bottles as weapons."
I tend to add here: feet, chairs, boards, etc. etc... and yes, if pressed I'd say staves. Basically any improvised or similar, or natural, weapon. Higher skill levels tend to indicate specific styles such as Judo, Wrestling, Boxing, etc. but that's just colour sub-text
The Traveller Book fleshes out the description a bit more which is probably where I sourced my expanded take:
"Brawling Weapons: Brawling generally involves found
or easily located weapons which are already at the site of
the brawl. Brawling weapons are effective only at close and
short range. Such weapons are classified as clubs, cost
nothing, and generally weigh from 500 to 3000 grams (one
die times 500 grams). Pistols may be used as clubs when
brawling. Bottles may be used as clubs (once, then they
become dagger minus 1). Animals are equipped with their
own weapons, generally specified in the encounter tables
which specify and define the animal."